The pool (Master+ mode). 31,000 players: 80 HC (High Challenger, 2500+ LP), 220 LC (Low Challenger, 2000–2500), 700 GM (Grandmaster, 1500–2000), 1,500 HM (High Master, 1000–1500), 5,000 MM (Mid Master, 500–1000), 23,500 LM (Low Master, 0–500).
MMR per tier (centred on LM = 0): HC +1275, LC +1000, GM +750, HM +500, MM +250, LM 0. Tier midpoints derived from LP cutoffs.
Diamond+ mode. Adds a 7th tier: DM (Diamond) at MMR −150. This is a working estimate (will be refined empirically as data accumulates). The choice of −150 implies a 5-Diamond team would win roughly 30% against a 5-LM team. Diamond+ mode does NOT show occurrence rates because shortly after the hard reset, matchmaking is no longer random selection from the full pool — it targets opponents close to your performance level, making static "1 in X" probabilities meaningless.
Team rating = soft-max with T = 400. R_team = T · log(Σ exp(R_i / T)). T = 400 means the strongest player only starts to dominate when they're a full tier or more above their teammates. Aggregator direction (lean toward MAX over AVG) is supported by Dehpanah et al. (2021).
Win probability uses standard Elo with S = 400. P = 1 / (1 + 10^((R_opp − R_team)/S)). A 400-point MMR gap makes the higher team 10× more likely to win.
Match-occurrence probability (Master+ mode only). Assumes uniform random sampling of 10 distinct players from the 31,000-player pool. Real Riot matchmaking targets balance, so genuinely lopsided matchups are even rarer in practice. Meaningful only right after a hard reset; once MMR data accumulates, occurrence numbers stop reflecting reality.
Why these row counts? Master+: C(10,5) = 252 distinct compositions across 6 tiers, 252² = 63,504 ordered matchups. Diamond+: C(11,5) = 462 compositions across 7 tiers, 462² = 213,444 ordered matchups.